Fig. 11.

Non-smooth problem involving a Dirac delta function ($f(\mathbf{x})=\frac{{\eta }^2}{{\left({\eta }^2,+,{\left|\left|\mathbf{x}\right|\right|}_2^2\right)}^2}$, $\mathbf{g}(\mathbf{x})=\mathbf{x}\sqrt{\frac{1+{\eta }^2}{{\eta }^2+{\left|\left|\mathbf{x}\right|\right|}_2^2}}$, $\eta =1/4$). Top left: Numerical approximation of the solution of the component $u_{1,h}$. Top right: Numerical approximation of the solution of the component $u_{2,h}$. Middle left: Numerical approximation of $det\mathrm{\nabla }{\mathbf{u}}_h$. Middle right: Numerical approximation of $det{\mathbf{p}}_h$. Bottom left: Visualization of $\left|\left|{\mathbf{u}}_h\right|\right|$. Bottom right: Visualization of the vector field ${\mathbf{u}}_h$. The results are obtained on structured mesh of the unit disk with $h=0.0209$ and $\epsilon =h^2$